We are considering a trip to Brazil for 2006 and our dates are extremely flexible. I was wondering, what would be the best month to visit Brazil. We would prefer not to travel from May through September though. We live in the Chicago area and have nice weather this time of year here. Thank you

Best months are April, May and October, November. Low season, less crowded. Both periods also have the nicest temperature.

I was wondering being Brazil such a big country, much larger than the continental US, can this question being answered without Lisa saying where she wants to go.
I imagine big difference between Rio and Manaos or Sao or Natal....just curious

I am looking to go to the Amazon, Iguazzu Falls, Rio, and a beach location (undecided yet) so I will be all over Brazil. Thanks

As amazing as it can be, although being larger than the USA, the variations in weather are not THAT extreme, i.e., there will be no time where you will freeze to death or it rains without mercy. For the locations you are thinking:
Amazon - ALWAYS hot and humid. Not much difference the time of the year you go.
Iguaçu Falls - There you can find cooler weather in winter (remember winter here is July-August). Cooler I mean 10 - 15 C.
Rio - Summer can be too hot. Sometimes 38-40 C (and that“s high season). Winter is very pleasant at 18-23C roughly (some people find it too cold for the beaches though).
Beach Location - If northeast of the country always good weather. Basically no difference between time of they year. Therefore, roughly speaking, weather can be good all over the year (with more chances of rain in summer) and the month you choose depends very much if you prefer crowds or not (also events like carnival, etc).